Certain motion blur often occurs to a captured image due to relative movement between a camera and a scene to capture. A model of image degradation may be expressed into the following convolution processI=L⊗k+N  (1)
where I denotes a captured blurry image, L denotes a latent image, k denotes a blur kernel (a point spread function, PSF), N denotes a noise of an image capturing device, and ⊗ denotes a convolution operator. In equation (1), only the blurry image I is known, such that a process of solving L by single image blind deconvolution is a highly ill-posed problem.
When a light source or a reflective object (e.g., water face, metal, glass, etc.) is present, the high-luminance points will form a light streak on an image, seriously degrading image quality. A blurry image with a light streak is a special case of motion blur images. In this case, if the luminance of the point light source or reflective point is so high to exceed a sensor threshold in an imaging device such that saturated pixels are formed on an imaging plane, each sensor response will be equal to a sensor saturation response, resulting in equation 2:k1=k2= . . . =kw= . . . kn=sensor saturation response  (2)
At this point, the blur model does not satisfy the linear convolution model of equation (1) and thus cannot be represented by convolution. A motion trajectory of a saturated target point along the camera on the imaging plane forms a light streak. Due to a relatively large contrast with a background region, the light streak has noticeable edges, while these noticeable edges will affect an edge map for estimating the blur kernel, leading to inaccurate estimation of the blur kernel. However, the light streak also provides useful information for blur kernel estimation.
Single image deblurring has attracted the attention of more and more researchers, and significant progress has been made. Because only a blurry image is known while what to obtain are a blur kernel and an unknown latent image, by constraining the unknown image based on the blur kernel characteristics such as sparsity and natural image statistical characteristics such as gradient distribution, the blur kernel and an intermediate image may be obtained; meanwhile these constraints may prevent trapping of the solving into local minima, which guarantees the blur kernel sparsity and denoises the restored image. In Literature [1], Fergus et al. took the initiative to take the blur kernel as a function to estimate the blur kernel using an ensemble learning method, where a variational Bayesian approach is adopted and a heavy-tailed distribution model of natural image gradients is represented with a Gaussian hybrid model. However, this method is relatively complex and has a very slow image processing process. In Literature [2], Krishnan et al. assumes a hyper-Laplacian distribution of the gradients of L, obtaining a high-quality restored image; the hyper-Laplacian constraint as an effective constraint is extensively applied to subsequent deblurring work.
Currently, not so many achievements in the researches on deblurring a blurry image including a light streak are available at home and abroad. Although the light streak includes much useful information (e.g., shape information of the blur kernel), such information is not effectively utilized in most deblurring algorithms. In Literature [3], Hua & Low manually selected a light streak region and used it to constrain the blur kernel; however, the manually selected image patch is not surely an image region suitable for constraining the blur kernel, which is highly dependent on human priors. In Literature [4], Hu et al. proposed an algorithm to deblur a night scene blurry image using light streak information, where an optimum light-streak image patch was automatically selected, and blur kernel estimation was performed in conjunction with other image priors; however, false detection and missed detection often occur to that method. Because the saturated pixels disrupt the linear convolutional model, the traditional deconvolution algorithm is not suitable for restoring such pictures. To address this issue, Whyte et al. in Literature [5] established a forward model to eliminate a ringing effect triggered by the saturated pixels. Cho et al. In literature [6] removed the saturated pixels to perform deconvolution operation using non-saturated pixels.
In view of the above, it is seen that single-image motion deblurring has received extensive attention, and many motion deblurring algorithms with significant application values have come out. A blurry image with a light streak provides blur kernel information. However, currently there still lacks a method of sufficiently extracting the light streak information in a blurry image, performing blur kernel estimation with the information to motion deblur the image, and thereby restoring a high-quality image.